It is known that an internal combustion engine of a motor vehicle generally includes a fuel injection system (FIS) including a fuel rail and a plurality of fuel injectors in fluid communication with the fuel rail and configured to perform fuel injections into the combustion chambers of the engine. The fuel injection system may further include a high pressure fuel pump, which may be embodied as a piston pump, driven by the engine and configured to perform a discharge stroke after every fuel injection, in order to deliver into the fuel rail a quantity of fuel that compensate for the injected fuel quantity.
The fuel injectors are essentially embodied as electromechanical valves having a needle, which is normally biased in a closed position by a spring, and an electro-magnetic actuator (e.g. solenoid), which moves the needle towards an open position in response to an energizing electrical current. The energizing electrical current is provided by an electronic control unit, which is generally configured to determine the fuel quantity to be injected by the fuel injection, to calculate the duration of the energizing electrical current (i.e. the energizing time) needed for injecting the desired fuel quantity, and finally to energize the fuel injector accordingly.
However, it may happen that the fuel quantity actually injected during a fuel injection is different from the desired fuel quantity. This unwanted condition may be caused by several factors, including drift of the injection characteristics and production spread of the fuel injectors. In particular, the correlation between the electrical command and the injector needle displacement can be affected by realities hard to control during injector manufacturing, such as magnetic permeability drift of the actuator, tolerance of the needle spring coefficient, aging effect, and temperature dependency. Accordingly, there is a need to provide a strategy for determining the quantity of fuel which is actually injected by a fuel injector during a fuel injection.